Rewrite as a simplified fraction. ${1.2\overline{76} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1276.7676...\\ 10x &= 12.7676...\end{align*}}$ Subtracting the two equations, we have: ${990x = 1264}$ ${x = \dfrac{1264}{990}} $ ${x = \dfrac{632}{495}} \text{or} {1 \dfrac{137}{495}}$